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We introduce the notion of arithmetic progression blocks or mAP blocks of Z n , which can be represented as sequences of the form (x, x + m, x + 2m,. .. , x + (i − 1)m) (mod n). Then we consider the problem of partitioning Z n into mAP blocks. We show that subject to a technical condition, the number of partitions of Z n into mAP blocks of a given type is… (More)

We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a+ b, a+ 2b,. .. , a+ nb is a polynomial in na+ n(n + 1)b/2. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of… (More)